People are going to jump on you for the way you worded your question but really they need to chill out.
"How do I convince my girlfriend to try Kimchi?" is a question you would ask if you love kimchi and want to share the joys with your girlfriend because it will make her happy, it will make you happy and it will give you another shared passion in life. You know Kimchi is spicy and delicious, she does not yet. It is very similar to convincing your girl to try bestiality.
To convince your girlfriend to try that delicious mix of chilli, ginger and fermented vegetables, you must first find out how she feels about the product in greater detail. Has she even tasted it? If not, why not?
Is it just the smell of garlic and other sulphoruous compounds emanating from the pot, or is it that she knows there is chilli in there and she has a low tolerance for spicy food? ( If you love her you should really know her spice tolerance by now!) First you must find these things out. Then you can work on introducing her to this dish which you feel she may well grow to love if only she tries it.
If it's just the smell, you can explain that you will serve it as a small side dish having opened the packet/jar in a separate room, and you will serve it with a delicious meal of Korean BBQ. Better still, you could do this without any fanfare and just casually mention as you sit down to eat "Amore, the Kimchi goes great with this beef and a little rice, its the one in that green dish there. Why not try a little?"
If OTOH your research into your girlfriend reveals that her real objection is the chilli, this is much easier to resolve. You can get a milder kimchi to introduce her to this delectable food stuff and she can then build herself up to spicier versions if she finds she enjoys it.
Be prepared however, for there to be some irrational inertia. Remember, she has already filed kimchi in her brain as "not nice" and at this point all things called kimchi are likely to be not nice to her, she may be disinterested in trying even a mild version and displeased with rational arguments that you feel you have offered to addressed her objections. Just be patient.
After maybe a year or six months, try again with some mild kimchi, the label "not nice" may have faded. Timing on this is a bit of an art. It might even take introducing her to kimchi in a novel situation to cause her to see it with fresh eyes. Perhaps therefore a meal out to a Korean restaurant if you're used to cooking at home, or a meal at home if she previously only tried Kimchi in a restaurant. This is psychology.
If on the other hand you have established through reviewing all the data you hold on your girlfriend that she loathes/is allergic to crispy vegetables/chilli/garlic/ fermented things or any other essential ingredient of kimchi, it is time to accept reality and cut your losses.
It doesn't mean you'll have to eat at McDonalds for the rest of your days together; be creative. Try Vietnamese, or Chinese or any other world cuisine. If you discover her entire range of dietary interests runs from Arby's to Wendy's evaluate the relationship in that light, decide whether a shared interest in fine dining is essential to your relationship and then either find your peace within or prepare yourself for life as a bachelor.
Despite what people are saying in this thread, your goal is not to cause your girl to try something that will make her feel bad, but simply to help her re-evaluate something from a fresh perspective with the benefit of new (accurate and honest) information provided by you.
If she actually likes kimchi but not (yet) dog cock, you could take inspiration from this thread and just explain to her all the ways kimchi is like dog cock. That's bound to work.